A monotone isomorphism theorem

• 成果类型: Article
• 署名作者: Soo, Terry
• 署名单位: University of Kansas
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0700-x
• 发表日期: 2017
• 页码: 1117-1136
• 关键词: bernoulli-shifts; ergodic-theory; entropy

摘要

In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary sequence to another that is coordinatewise smaller than or equal to the original sequence.